NYC apartment hunting - real estate agent question

[James Schiaffo]

Looking to move into a new apartment (hopefully next week.) When we found the apartment, the real estate agent told us it comes with one month free. Fast forward to lease day, inside the lease there is no mention of the free month.

On top of the lease, was a letter from the management company to our real estate agent, that says,

“Enclosed, please find a New lease for apartment ***. All tenants have to sign all lease copies, including riders. One month rent, one month security deposit and carbon monoxide detector is due at signing.”

The real estate agent we are working with said he will write something on the letter to state we are supposed to receive one month free and he will sign it.

I am not expert, which is why I am here but is he legally able to sign a hand written note on top of this letter and it will bind the management company ? 

Please help, thank you.